Signal filtering

ABSTRACT

A method of filtering an information signal (x(t)), the method comprising modifying frequency domain components (X(k,n)) of the information signal according to a desired filter response (F(k,n)); wherein the step of modifying frequency domain components further comprises modifying ( 105 ) frequency domain components of a first frame of said information signal according to a first actual filter response (F′(k,n)), the first actual filter response being a function (Φ) of the desired filter response and information ( 108 ) related to a previous frame of the information signal.

This invention relates to the filtering of an information signal and, inparticular, to the filtering of an information signal by modifyingfrequency domain components of the information signal according to adesired filter response.

In the field of signal processing, it is known to perform a filtering ofan information signal, such as an audio signal, by segmenting theinformation signal using overlapping frames, transforming the framesinto the frequency domain, modifying the frequency-domain components ofthe signal frame, inverse transforming the modified frequency-domaincomponents back into the time domain, and performing an overlap-addoperation (see e.g. Oppenheim & Shafer: “Discrete-time signalprocessing”, Prentice Hall signal processing series, 1989).

The above prior art involves the problem that the overlap-add operationof successive frames may result in undesirable artifacts, if thefiltering step, i.e. the modification of the frequency-domaincomponents, includes a processing with dynamically varying parameters,in particular with a varying phase. For example, it may happen that acertain frequency component adds in-phase for the overlap of twoconsecutive frames n and n+1, while the same components may beout-of-phase, if frame n+1 is compared to n+2. In the case of audiosignals, these artifacts may result in unstable sound quality, e.g.modulations. In general, such artifacts may occur for any block-basedimplementation, i.e. an implementation where a filter transform isupdated at a rate lower than the sample rate of the signal, therebygenerating artifacts due to block-varying phases.

The above and other problems are solved by a method of filtering aninformation signal, the method comprising modifying frequency domaincomponents of the information signal according to a desired filterresponse; wherein the step of modifying frequency domain componentsfurther comprises modifying frequency domain components of a first frameof said information signal according to a first actual filter response,the first actual filter response being a function of the desired filterresponse and information related to a previous frame of the informationsignal.

Hence, by modifying the frequency domain components of a current signalframe according to an actual filter response which is a function of thedesired filter response and information related to a previous frame ofthe information signal, the filter response of a processing step istransformed taking a previous processing step into consideration.Consequently, artifacts due to phase changes across consecutive framesare efficiently reduced.

In general, the processing of a filter may be described by its filterresponse. In the frequency domain, the filter output for a givenfrequency component may be expressed as a corresponding input frequencycomponent multiplied with a, in general complex, filter response orweight factor. The term desired filter response comprises the filterresponse or weight factors corresponding to the desired filter function.Methods for determining desired filter responses for a given filter areknown in the art of signal processing (see e.g. Oppenheim & Shafer,“Discrete-time signal processing”, Prentice Hall signal processingseries, 1989). The term actual filter response comprises the filterresponse actually applied to the input signal according to theinvention.

In a preferred embodiment of the invention, the method further comprises

segmenting an information signal into a number of signal frames;

transforming the signal frames to obtain frequency domain components ofthe respective signal frames;

inverse transforming the modified frequency domain components to obtainfiltered signal frames; and

performing a recombination operation of the filtered signal frames toobtain a filtered information signal.

Hence, an efficient filtering method is provided which reduces theamount of distortions introduced due to the filtering.

Preferably, the function of the desired filter response and informationrelated to a previous frame is selected as to reduce artifactsintroduced by the step of performing a recombination operation, therebyimproving the perceptual quality of the information signal.

Here, the term recombination operation comprises any recombinationtechnique for recombining the modified signal from the modified signalframes. Examples of such recombination operations comprise anoverlap-add method, an overlap-save method, or the like.

The information related to a previous frame may comprise a filterresponse of a previous frame, the modified frequency components of aprevious frame, or the like.

In a preferred embodiment, the information related to a previous framecomprises at least one of the actual filter response and the desiredfilter response of a previous frame of the information signal. Hence theactual filter response may be a function of the desired filter responseof one or more previous frames and/or the actual filter response appliedto one or more previous frames, thereby providing a method which may beadapted to a large variety of applications.

It is noted that the function may further depend on additionalinformation, such as information about the current frame, e.g. atonality measure of the current flame.

In another preferred embodiment, the step of modifying frequency domaincomponents of a first frame further comprises

determining a desired filter response for the first frame;

determining the first actual filter response for the first frame as afunction of the desired filter response and at least a second filterresponse related to a previous frame of the information signal; and

applying the determined actual first filter response to the first frameto obtain modified frequency domain components of the first frame.

It is further preferred that the function of the desired filter responseand the second filter response is selected as to reduce phase changes ofthe filter response.

In a further preferred embodiment, the step of determining the firstactual filter response comprises

determining a phase difference of a frequency component of the desiredfilter response for the first frame and a corresponding frequencycomponent of the filter response of a previous frame;

determining a desired phase change as a function of the determined phasedifference; and

determining a frequency component of the first actual filter response asthe corresponding frequency component of the filter response of aprevious frame modified by a phase change factor comprising thedetermined desired phase change.

Hence, a method is provided for efficiently limiting the phase change ofthe filter response between consecutive frames, thereby reducingperceptible artifacts in the resulting signal.

In a yet further preferred embodiment, the function of the determinedphase difference is a cut-off function limiting the phase difference tobe smaller than a predetermined threshold value. Hence a determinationof the phase difference is provided that only requires littlecomputational resources. Furthermore, as the threshold value may beselected according to the actual application, e.g. as a fixed value, atime and/or frequency dependant value, or the like, the method may beadapted to a variety of applications. Alternatively, other relationsbetween the determined and the desired phase difference may be chosen,e.g. a soft-knee behavior provided by a saturated input-output function.

In a yet further preferred embodiment, said reduction of phase changesof the filter response is made dependant on a measure of tonality. Forexample, for a noise-like signal, phase jumps between consecutivesamples may occur in the input signal. Limiting the phase difference forsuch samples may change the perceptual properties of the filtered signalin an undesired way. For example, in the case of audio signals, anoise-like signal would become more tonal which is often perceived as asynthetic or metallic sound. Hence by only—or at leastpredominantly—limiting the phase difference of signal frames having ahigh level of tonality, the above undesired effects may be reduced.

The present invention can be implemented in different ways including themethod described above and in the following, an arrangement, and furtherproduct means, each yielding one or more of the benefits and advantagesdescribed in connection with the first-mentioned method, and each havingone or more preferred embodiments corresponding to the preferredembodiments described in connection with the first-mentioned method anddisclosed in the dependant claims.

It is noted that the features of the method described above and in thefollowing may be implemented in software and carried out in a dataprocessing system or other processing means caused by the execution ofcomputer-executable instructions. The instructions may be program codemeans loaded in a memory, such as a RAM, from a storage medium or fromanother computer via a computer network. Alternatively, the describedfeatures may be implemented by hardwired circuitry instead of softwareor in combination with software.

The invention further relates to an arrangement for filtering aninformation signal, the arrangement comprising means for modifyingfrequency domain components of the information signal according to adesired filter response; wherein the means for modifying frequencydomain components of the information signal comprises means formodifying frequency domain components of a first frame of saidinformation signal according to a first actual filter response, thefirst actual filter response being a function of the desired filterresponse and information related to a previous frame of the informationsignal.

It is noted that the above arrangement including the means for modifyingthe frequency components may be implemented as general- orspecial-purpose programmable microprocessors, Digital Signal Processors(DSP), Application Specific Integrated Circuits (ASIC), ProgrammableLogic Arrays (PLA), Field Programmable Gate Arrays (FPGA), specialpurpose electronic circuits, etc., or a combination thereof.

The invention further relates to an electronic device comprising such anarrangement. The term electronic device comprises any device suitablefor the processing of an information signal. Examples of such devicescomprise audio equipment including an audio decoder for decoding codedaudio information, such as audio players, recorders, etc.

The invention further relates to a filtered information signal generatedby the method described above and in the following. The filteredinformation signal may further be processed, e.g. coded according to aknown coding scheme, such as an MPEG coding scheme.

The invention further relates to a storage medium having stored thereonsuch a filtered information signal.

Here, the term storage medium comprises but is not limited to a magnetictape, an optical disc, a digital video disk (DVD), a compact disc (CD orCD-ROM), a mini-disc, a hard disk, a floppy disk, a ferro-electricmemory, an electrically erasable programmable read only memory (EEPROM),a flash memory, an EPROM, a read only memory (ROM), a static randomaccess memory (SRAM), a dynamic random access memory (DRAM), asynchronous dynamic random access memory (SDRAM), a ferromagneticmemory, optical storage, charge coupled devices, smart cards, a PCMCIAcard, etc.

These and other aspects of the invention will be apparent and elucidatedfrom the embodiments described in the following with reference to thedrawing in which:

FIG. 1 illustrates a method of filtering an information signal accordingto an embodiment of the invention;

FIG. 2 illustrates an embodiment of the transformation of the filterresponse;

FIG. 3 illustrates examples of functional forms used in the embodimentof FIG. 2; and

FIG. 4 illustrates another embodiment of the transformation of thefilter response.

FIG. 1 illustrates a method of filtering an information signal accordingto an embodiment of the invention. In an initial step 101, an incominginformation signal x(t) is segmented into a number of frames. Theincoming signal is assumed to be a suitably sampled waveform, e.g.representing an audio signal or the like. For example, in the case of anaudio signal, t represents a discrete time. Therefore, we will refer tosignals indexed by t as signals in the time domain. However, it isunderstood that, for other types of information signals, t may representother coordinates, such as spatial coordinates. The segmentation step101 splits the signal into frames x_(n)(t) of a suitable length, forexample in the range 500-5000 samples, e.g. 1024 or 2048 samples.Preferably, the segmentation is performed using overlapping windowfunctions, thereby suppressing artefacts which may be introduced at theframe boundaries (see e.g. Princen, J. P., and Bradley, A. B.:“Analysis/synthesis filterbank design based on time domain aliasingcancellation”, IEEE transactions on Acoustics, Speech and Signalprocessing, Vol. ASSP 34, 1986).

In step 102, each of the frames x_(n)(t) is transformed into thefrequency domain by applying a Fourier transformation, preferablyimplemented as a Fast Fourier Transform (FFT). The resulting frequencyrepresentation of the n-th frame x_(n)(t) comprises a number offrequency components X(k,n) where the parameter-n indicates the framenumber and the parameter k indicates the frequency component orfrequency bin corresponding to a frequency ω_(k), 0<k<K. In general, thefrequency domain components X(k,n) are complex numbers.

In step 103, the desired filter for the current frame is determined. Inmany applications the calculation of the desired filter is performedadaptively, i.e. in response to predetermined properties of the incomingsignal, or controlled by time-varying parameters, i.e. in response toother signals or parameters, or the like. For example, in the field ofparametric audio coding a stereo signal is often synthesized from acoded mono signal and predetermined additional parameters, such as acorrelation between the left and right channels, etc. During synthesisof the stereo signal, each channel is filtered according to the desiredproperties of the resulting stereo signal. In another example, receivedcommunications signals are often filtered according to estimated channelproperties.

The desired filter is expressed as a desired filter response comprisinga set of K complex weight factors F(k,n), 0<k<K, for the n-th frame. Thefilter response F(k,n) may be represented by two real numbers, i.e. itsamplitude a(k,n) and its phase φ(k,n) according toF(k,n)=a(k,n) exp[jφ(k,n)].

In the frequency domain, the filtered frequency components areY(k,n)=F(k,n)·X(k,n), i.e. they result from a multiplication of thefrequency components X(k,n) of the input signal with the filter responseF(k,n). As will be apparent to a skilled person, this multiplication inthe frequency domain corresponds to a convolution of the input signalframe x_(n)(t) with a corresponding filter f_(n)(t).

According to the invention, in step 104, the desired filter responseF(k,n) is modified before applying it to the current frame X(k,n). Inparticular, the actual filter response F′(k,n) to be applied isdetermined as a function of the desired filter response F(k,n) and ofinformation 108 about previous frames. Preferably, this informationcomprises the actual and/or desired filter response of one or moreprevious frames, according toF^(′)(k, n) = a^(′)(k, n) ⋅ exp [jφ^(′)(k, n)] = Φ[F(k, n), F(k, n − 1), F(k, n − 2), …  , F^(′)(k, n − 1), F^(′)(k, n − 2), …  ].

Hence, by making the actual filter response dependant of the history ofprevious filter responses, artifacts introduced by changes in the filterresponse between consecutive frames may be efficiently suppressed.Preferably, the actual form of the transform function Φ is selected toreduce overlap-add artifacts resulting from dynamically-varying filterresponses.

For example, the transform function Φ may be a function of a singleprevious response function, e.g. F′(k,n)=Φ₁[F(k,n), F(k,n-1)] orF′(k,n)=Φ₂[F(k,n), F′(k,n-1)]. In another embodiment, the transformfunction may comprise a floating average over a number of previousresponse functions, e.g. a filtered version of previous responsefunctions, or the like. Preferred embodiments of the transform functionΦ will be described in greater detail below.

In step 105, the actual filter response F′(k,n) is applied to thecurrent frame by multiplying the frequency components X(k,n) of thecurrent frame of the input signal with the corresponding filter responsefactors F′(k,n) according toY(k,n)=F′(k,n)·X(k,n).

In step 106, the resulting processed frequency components Y(k,n) aretransformed back into the time domain resulting in filtered framesy_(n)(t). Preferably, the inverse transform is implemented as an InverseFast Fourier Transform (IFFT).

Finally, in step 107, the filtered frames are recombined to a filteredsignal y(t) by an overlap-add method. An efficient implementation ofsuch an overlap add method is disclosed in Bergmans, J. W. M.: “Digitalbaseband transmission and recording”, Kluwer, 1996.

FIG. 2 illustrates an embodiment of the transformation of the filterresponse. According to this embodiment, the transform function Φ of step104 in FIG. 1 is implemented as a phase-change limiter between thecurrent and the previous frame.

In step 201, the phase change δ(k) of each frequency component F(k,n)compared to the actual phase modification φ′(k,n-1) applied to theprevious sample of the corresponding frequency component is computed,i.e.δ(k)=φ(k,n)−φ′(k,n-1).

In step 202, the phase component of the desired filter F(k,n) ismodified in such a way that the phase change across frames is reduced,if the change would result in overlap-add artifacts. According to thisembodiment, this is achieved by ensuring that the actual phasedifference does not exceed a predetermined threshold c, e.g. by simplycutting of the phase difference, according to $\begin{matrix}{\left( {k,n} \right) = \left\{ \begin{matrix}{F\left( {k,n} \right)} & {{{if}{{\delta(k)}}} < c} \\{{{F^{\prime}\left( {k,{n - 1}} \right)}.{\mathbb{e}}^{j.c.{{sign}{\lbrack{\delta{(k)}}\rbrack}}}},} & {otherwise}\end{matrix} \right.} & (1)\end{matrix}$

The threshold value c may be a predetermined constant, e.g. between π/8and π/3 rad. In one embodiment, the threshold c may not be a constantbut e.g. a function of time, frequency, and/or the like. Furthermore,alternatively to the above hard limit for the phase change, otherphase-change-limiting functions may be used.

FIG. 3 illustrates examples of functional forms used in the embodimentof FIG. 2. In general, in the above embodiment, the desired phase-changeacross subsequent time frames for individual frequency components istransformed by an input-output function P(δ(k)) and the actual filterresponse F′(k,n) is given byF′(k,n)=F′(k,n-1)·exp[j P(δ(k))].   (2)

Hence, according to this embodiment, a transform function P of the phasechange across subsequent time frames is introduced.

FIG. 3 illustrates two examples of functional forms of the transformfunction P. The solid curve illustrates the hard limit described above,which limits the phase change to be smaller than the threshold c, asillustrated by the dotted lines 303. As an alternative to the above“hard-knee” input-output relation, a “soft-knee” input-output relationmay be used as illustrated by the dashed line 302 in FIG. 3. Such asmooth transition may be implemented by a differentiable, monotonousfunction, e.g. P(x)=c tan h(αx), where c is the above threshold and theparameter a determines the slope of the curve.

Again referring to FIG. 2, in step 203, the actual filter responseF′(k,n) is determined according to eqn. (2) above.

FIG. 4 illustrates another embodiment of the transformation of thefilter response. According to this embodiment, the phase limitingprocedure is driven by a suitable measure of tonality, e.g. a predictionmethod as described below. This has the advantage that phase jumpsbetween consecutive frames which occur in noise-like signals may beexcluded from the phase-change limiting procedure according to theinvention. This is an advantage, since limiting such phase jumps innoise like signals would make the noise-like signal sound more tonalwhich is often perceived as synthetic or metallic.

According to the embodiment of FIG. 4, in step 401, a predicted phaseerrorθ(k)=φ(k,n)−φ(k,n-1)−ω_(k) ·his calculated. Here, ω_(k) denotes the frequency corresponding to thek-th frequency component and h denotes the hop size in samples. Here,the term hop size refers to the difference between two adjacent windowcenters, i.e. half the analysis length for symmetric windows. In thefollowing, it is assumed that the above error is wrapped to the interval[−π,+π].

In step 402, a prediction measure P_(k) for the amount of phasepredictability in the k-th frequency bin is calculated according toP _(k)=(π−|θ(k)|)/π∈[0,1],where |·| denotes the absolute value.

Hence, the above measure P_(k) yields a value between 0 and 1corresponding to the amount of phase-predictability in the k-thfrequency bin. If P_(k) is close to 1, the underlying 5 signal may beassumed to have a high degree of tonality, i.e. has a substantiallysinusoidal waveform. For such a signal, phase jumps are easilyperceivable, e.g. by the listener of an audio signal. Hence, phase jumpsshould preferably be removed in this case. On the other hand, if thevalue of P_(k) is close to 0, the underlying signal may be assumed to benoisy. For noisy signals phase jumps are not easily perceived and may,therefore, be allowed.

Accordingly, in step 403, the phase limiting function is applied ifP_(k) exceeds a predetermined threshold, i.e. P_(k)>A, resulting in theactual filter response F′(k,n). For example, a phase limiting functionas described in connection with FIGS. 2 and 3 may be applied if P_(k)>A,according to ${F^{\prime}\left( {k,n} \right)} = \left\{ {\begin{matrix}{F\left( {k,n} \right)} & {{{if}\quad P_{k}} < A} \\{{{F^{\prime}\left( {k,{n - 1}} \right)} \cdot {\mathbb{e}}^{j \cdot {P{\lbrack{\delta{(k)}}\rbrack}}}},} & {otherwise}\end{matrix}.} \right.$

Here, A is limited by the upper and lower boundaries of P which are +1and 0, respectively. The exact value of A depends on the actualimplementation. For example, A may be selected between 0.6 and 0.9.

It is understood that, alternatively, any other suitable measure forestimating the tonality may be used. In yet another embodiment, theallowed phase jump c described above may be made dependant on a suitablemeasure of tonality, e.g. the measure P_(k) above, thereby allowing forlarger phase jumps if P_(k) is large and vice versa

It is noted that the above methods may be implemented by correspondingarrangements, e.g. implemented as general- or special-purposeprogrammable microprocessors, Digital Signal Processors (DSP),Application Specific Integrated Circuits (ASIC), Programmable LogicArrays (PLA), Field Programmable Gate Arrays (FPGA), special purposeelectronic circuits, etc., or a combination thereof Hence, FIGS. 1, 2,and 4 above may be read as block diagrams of such arrangements.

It should further be noted that the above-mentioned embodimentsillustrate rather than limit the invention, and that those skilled inthe art will be able to design many alternative embodiments withoutdeparting from the scope of the appended claims.

It should further be noted that even though the invention has primarilybeen described in connection with an audio signal, the scope of theinvention is not restricted to audio signals. It is understood that theinvention may also be applied to other information signals, such asmultimedia signals, video signals, animations, graphics, still images,or the like.

The method according to the invention may be applied to the filtering ofa large variety of information signals. As an example, the method may beapplied in the field of parametric stereo coding. As is known in thefield of parametric stereo coding, in a decoder of such a coding system,two output signals are synthesized, both having time-varying phasemodifications. Using the method according to the present invention, theinventors have observed a considerable improvement of the quality of thesynthesized output signals of such a system.

In the claims, any reference signs placed between parentheses shall notbe construed as limiting the claim. The word “comprising” does notexclude the presence of elements or steps other than those listed in aclaim. The word “a” or “an” preceding an element does not exclude thepresence of a plurality of such elements.

The invention can be implemented by means of hardware comprising severaldistinct elements, and by means of a suitably programmed computer. Inthe device claim enumerating several means, several of these means canbe embodied by one and the same item of hardware. The mere fact thatcertain measures are recited in mutually different dependent claims doesnot indicate that a combination of these measures cannot be used toadvantage.

1. A method of filtering an information signal, the method comprisingmodifying frequency domain components of the information signalaccording to a desired filter response; wherein the step of modifyingfrequency domain components further comprises modifying frequency domaincomponents of a first frame of said information signal according to afirst actual filter response, the first actual filter response being afunction of the desired filter response and information; related to aprevious frame of the information signal.
 2. A method according to claim1, wherein the method further comprises segmenting an information signalinto a number of signal frames; transforming the signal frames to obtainfrequency domain components of the respective signal frames; inversetransforming the modified frequency domain components to obtain filteredsignal frames; and performing a recombination operation of the filteredsignal frames to obtain a filtered information signal.
 3. A methodaccording to claim 2, wherein the function of the desired filterresponse and information related to a previous frame is selected as toreduce artifacts introduced by the step of performing a recombinationoperation.
 4. A method according to claim 2, wherein the recombinationoperation comprises an overlap-add operation.
 5. A method according toclaim 1, wherein the information related to a previous frame iscomprises at least one of the actual filter response and the desiredfilter response of a previous frame of the information signal.
 6. Amethod according to claim 1, wherein the step of modifying frequencydomain components of a first frame further comprises determining adesired filter response for the first frame; determining the firstactual filter response for the first frame as a function of the desiredfilter response and at least a second filter response related to aprevious frame of the information signal; and applying the determinedactual first filter response to the first frame to obtain modifiedfrequency domain components of the first frame.
 7. A method according toclaim 6, wherein the step of determining the first actual filterresponse comprises determining a phase difference of a frequencycomponent of the desired filter response for the first frame and acorresponding frequency component of the filter response of a previousframe; determining a desired phase change as a function of thedetermined phase difference; and determining a frequency component ofthe first actual filter response as the corresponding frequencycomponent of the filter response of a previous frame modified by a phasechange factor comprising the determined desired phase change.
 8. Amethod according to claim 7, wherein the function of the determinedphase difference is a cut-off function limiting the phase difference tobe smaller than a predetermined threshold value.
 9. A method accordingto claim 6, wherein the function of the desired filter response andinformation related to a previous frame is selected to reduce phasechanges of the filter response.
 10. A method according to claim 9,wherein said reduction of phase changes of the filter response is madedependant on a measure of tonality.
 11. A method according to claim 1,wherein the information signal is an audio signal.
 12. An arrangementfor filtering an information signal, the arrangement comprising meansfor modifying frequency domain components of the information signalaccording to a desired filter response; wherein the means for modifyingfrequency domain components of the information signal comprises meansfor modifying frequency domain components of a first frame of saidinformation signal according to a first actual filter response, thefirst actual filter response being a function of the desired filterresponse and information related to a previous frame of the informationsignal.
 13. An electronic device comprising an arrangement for filteringan information signal, the arrangement comprising means for modifyingfrequency domain components of the information signal according to adesired filter response; wherein the means for modifying frequencydomain components of the information signal comprises means formodifying frequency domain components of a first frame of saidinformation signal according to a first actual filter response, thefirst actual filter response being a function of the desired filterresponse and information related to a previous frame of the informationsignal.
 14. A filtered information signal generated by a method offiltering an information signal, the method comprising modifyingfrequency domain components of the information signal according to adesired filter response; wherein the step of modifying frequency domaincomponents further comprises modifying frequency domain components of afirst frame of said information signal according to a first actualfilter response, the first actual filter response being a function ofthe desired filter response and information related to a previous frameof the information signal.
 15. A storage medium having stored thereon ainformation signal according to claim 14.